cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A290535 Determinant of circulant matrix of order 6 with entries in the first row (-1)^(j-1)*Sum_{k>=0} (-1)^k*binomial(n, 6*k + j - 1), j=1..6.

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%I A290535 #26 Aug 10 2018 02:36:12
%S A290535 1,0,0,0,0,0,-104284,-783050688,-329029322076,-43271152876224,
%T A290535 -2175830808446736,0,5427970251634650916,307609249050423946080,
%U A290535 8866068073884849492756,137518739026000524646272,896278292839676023110288,0,-2518571790589921864549097500
%N A290535 Determinant of circulant matrix of order 6 with entries in the first row (-1)^(j-1)*Sum_{k>=0} (-1)^k*binomial(n, 6*k + j - 1), j=1..6.
%C A290535 a(n) = 0 for n == 5 (mod 6).
%H A290535 Vladimir Shevelev, <a href="https://arxiv.org/abs/1706.01454">Combinatorial identities generated by difference analogs of hyperbolic and trigonometric functions of order n</a>, arXiv:1706.01454 [math.CO], 2017.
%H A290535 Wikipedia, <a href="https://en.wikipedia.org/wiki/Circulant_matrix">Circulant matrix</a>
%t A290535 ro[n_] := Table[(-1)^(j-1) Sum[(-1)^k Binomial[n, 6k+j-1], {k, 0, n/6}], {j, 1, 6}];
%t A290535 M[n_] := Table[RotateRight[ro[n], m], {m, 0, 5}];
%t A290535 a[n_] := Det[M[n]];
%t A290535 Table[a[n], {n, 0, 18}] (* _Jean-François Alcover_, Aug 10 2018 *)
%Y A290535 Cf. A290285, A290286.
%K A290535 sign
%O A290535 0,7
%A A290535 _Vladimir Shevelev_ and _Peter J. C. Moses_, Aug 05 2017